The first digit is the most important. It indicates the "level" of the course: 100/1000 courses are freshman level, 200/2000 are sophomore level, etc. There is some flexibility in these classifications, though. Examples: My undergraduate university used 1000 for intro level, 2000 for intermediate level, 4000 for senior/advanced level, and 6000 for graduate level. (3000 and 5000 were reserved for courses at a satellite campus.) My graduate university uses 100, 200, 300, 400 for the corresponding undergraduate year levels, and 600, 700, 800 for graduate courses of increasing difficulty levels. The other digits in the course number often indicate the rough order in which courses should be taken within a level. This is not always the case; sometimes they are just arbitrary, or they may indicate the order in which courses were added to the institute's offerings. In general, though the numbers indicate the levels of the courses and the order in which they "should" be taken, students' schedules need not comply precisely (outside of course-specific prerequisite requirements).

It varies from institution to institution, but generally the first number indicates the year you're likely to study it, so "Psychology 101" is the first course you're likely to study in your first year of a degree involving psychology, which is why it's the introduction to the subject. The numbering gets messy for a variety of reasons. I should point out I'm not an American university student, but this style of numbering system is becoming prevalent throughout the English-speaking world.